The Wumpus World:
Navigating Uncertainty with
Logic
A compact, visual guide to the Wumpus World formulation, a concrete
example, and three core forms of reasoning an intelligent agent uses to
survive and succeed.
PEAS Description
PEAS stands for Performance Measures, Environment, Actuators and
Sensors which describe agent’s capabilities and environment.
1. Performance measures: Rewards or Punishments
•
Agent gets gold and return back safe = +1000 points
•
Agent dies (pit or Wumpus)= -1000 points
•
Each move of the agent = -1 point
•
Agent uses the arrow = -10 points
The AI Agent's Challenge: A Perilous Cave
Environment
Objective
Hazards
Start
4×4 grid of rooms
Find the gold and
Wumpus (single
Starts at square
representing a cave.
return to the start
deadly monster)
(1,1) facing East —
The agent explores
to climb out safely.
and bottomless
only known square
one square at a
pits. One mistake
initially.
time.
can be fatal.
Agent's Perceptions: Clues in the Dark
Stench
Breeze
Glitter
Indicates the Wumpus occupies
Signals a pit in an adjacent
Gold is present in the current
an adjacent square (N, S, E or
square.
square.
W).
Bump
Scream
Agent attempted to move into a
Heard when the Wumpus dies
wall — updates map
(arrow hit) — removes the
boundaries.
Wumpus as a hazard.
Agent's Actions: Tools for Survival
Turn Left / Turn
Right
Forward
Grab
Shoot
Move one square in the
Pick up gold if present in
Fire one arrow straight
Change orientation
facing direction (may
the current square.
ahead to try to kill the
without leaving the
cause Bump).
square.
Climb
Exit the cave from the start square to finish the run.
Wumpus at unknown
distance.
Example:
Key Elements:
•
Pits: If the agent steps into a pit it falls and dies. A breeze
in adjacent rooms suggests nearby pits.
•
Wumpus: A creature that kills agent if it enters its room.
Rooms next to the Wumpus have a stench. Agent can
use an arrow to kill the Wumpus.
•
Treasure: Agent’s main objective is to collect the treasure
(gold) which is located in one room.
•
Breeze: Indicates a pit is nearby.
•
Stench: Indicates the Wumpus is nearby.
The Core Problem: Reasoning
Under Uncertainty
The Wumpus World is partially observable: the agent perceives only local
clues. It is deterministic: actions have predictable effects. The agent must
represent beliefs, update them, and infer hidden facts to plan safe
actions.
Key concepts used: knowledge representation, belief state,
logical inference, search and planning under uncertainty.